laurens grandpa has her pick a handful of change, she picks only nickels, dimes and quarters. lauren has 5 more quarters than dimes, and half as many nickels as quarters. if her total amt is $4.75 how many of each coin does lauren pick?
No idea either
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To solve the problem, we need to set up a system of equations based on the given information. Let's represent the number of nickels, dimes, and quarters that Lauren picked as N, D, and Q, respectively.
From the problem, we know that:
1) Lauren has 5 more quarters than dimes, so Q = D + 5.
2) Lauren has half as many nickels as quarters, so N = (1/2)Q.
3) The total value of the change is $4.75. The value of each nickel is $0.05, each dime is $0.10, and each quarter is $0.25. So, the equation representing the total value of the change is:
0.05N + 0.10D + 0.25Q = 4.75.
Now, let's substitute equations (1) and (2) into equation (3):
0.05[(1/2)Q] + 0.10D + 0.25Q = 4.75.
Simplify and solve for Q:
0.025Q + 0.10D + 0.25Q = 4.75,
0.275Q + 0.10D = 4.75,
275Q + 100D = 4750.
Now, let's apply the substitution Q = D + 5:
275(D + 5) + 100D = 4750,
275D + 1375 + 100D = 4750,
375D = 4750 - 1375,
375D = 3375,
D = 3375 / 375,
D = 9.
Now, substitute the value of D back into equation (1) to find Q:
Q = D + 5,
Q = 9 + 5,
Q = 14.
Finally, substitute the value of Q into equation (2) to find N:
N = (1/2)Q,
N = (1/2)14,
N = 7.
So, Lauren picked 7 nickels, 9 dimes, and 14 quarters.